Transcript Computation of the closed line traverse

Surveying I.
Lecture 10.
Traversing
Principle of Traversing
deflection angle
dS1
S
1
d23
d12
3
traverse point
2
traverse legs
• Determine the WCB of the first leg;
• measure the length of the first leg;
• compute the coordinates of the traverse point No. 1,
using the 1st fundamental task of surveying;
• measure the deflection angle at point 1;
• compute the WCB of the second leg;
• continue with step 2.
Types of traverse lines
Closed Loop
Unclosed
• Free traverse
• Inserted traverse
• Closed line traverse
Computation of the closed line traverse
T1
WCBS1
S
d S1
T2
1
1
3
2
d 12
2
d 23
3
E
d 3E
Controlling the angular observations:
• sum of the inner angles
WCBS1  1   2  3   E  90  90
• theory
n  2  2180
E
WCBE3
Computation of the closed line traverse
Angular misclosure:
  n 180  WCBS 1  1   2   3   E  90  90

 n 1 
  n  1 180     i ,
 i 0 
where  0  WCBS 1
How to correct for the angular error?
The accuracy of the angular observations can supposed to be
at the same level, therefore the same correction should be
applied to each observed angle (n).
v 

n
 i   i  v
Computation of the closed line traverse
T1
1
0
S
T2
d S1
1
3
2
d 12
2
d 23
3
E
d 3E
E
Controlling the distance observations:
• the computed coordinate differences between S
and E should be equal to the known coordinate
differences
Computation of the closed line traverse
Compute the provisional WCB of the traverse legs:
WCBi ,i 1  WCBi 1,i   i  180
Easting and Northing coordinate differences:
Ei ,i 1  di ,i 1  sin WCBi ,i 1 ,
N i ,i 1  d i ,i 1  cos WCBi ,i 1.
The coordinate misclosure:
n2
E  EE  ES    d i ,i 1  sin WCBi ,i 1
i 0
n2
N  N E  N S    d i ,i 1  cos WCBi ,i 1
The linear misclosure:
i 0
L  E 2  N 2
Computation of the closed line traverse
How to correct for the coordinate misclosure?
• coordinate error is caused by the distance
observations;
• the accuracy of distance observations is proportional
with the distance.
Corrections of the computed coordinate differences:
vEi ,i 1 
d i ,i 1  E
n2
d
i 0
vN i ,i 1 
i ,i 1
d i ,i 1  N
n2
d
i 0
,
i ,i 1
.
Computation of the closed line traverse
Computing the corrected coordinate differences:
Ei,i 1  Ei ,i 1  vEi ,i 1 ,
N i,i 1  N i ,i 1  vN i ,i 1.
Computing the final coordinates:
Ei 1  Ei  Ei,i 1 ,
Ni 1  Ni  Ni,i 1.
Computation of the inserted traverse
1
S
d S1
1
3
2
d 12
2
d 23
3
d 3E
S and E are known, the distances and the deflection
angles are measured.
No corrections for the angles (due to the lack of
orientations at the endpoints).
Corrections to the distance observations can be
computed due to the given endpoints.
E
Computation of the inserted traverse
*
3
*
3
2
S
d
23
*
1
WCBS1
WCB*
d S1
d ’S1
E
d 3E
*
d 12
11
1
d ’12
2
3
2
2
d ’23
3
d ’3E
The coordinates are computed as a free traverse by
using an abritrary starting WCB (WCB*).
E
Computation of the inserted traverse
Computing the correction to the starting WCB:
WCB  WCBSE  WCBSE
Computing the correction to the length of the
traverse legs (scale factor):
d SE
m
d SE
Computation of the inserted traverse
*
3
d 3E
*
3
2
S
d
23
*
1
WCBS1
WCB*
d S1
d ’S1
E
*
d 12
11
1
d ’12
2
3
2
2
d ’23
3
d ’3E
E
Computing the coordinates as a free traverse using
the following values:
WCBS1  WCB  WCB,
di,i 1  m  di ,i 1.
Localizing blunders in the observations
Distance observations
Compute the WCB of the linear misclosure. The
blunder is made most likely on the traverse leg, which
has a similar provisional WCB.
Angular observations
If only one blunder occurs in the observations, it can
be localized in case of a closed line traverse.
Compute the traverse as a free traverse in the
direction of S->E and E->S as well. The blunder is
made at the station, which has similar coordinates in
both solutions.
Thank You for Your Attention!